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We consider $d$-dimensional static spacetimes in Einstein gravity with acosmological constant in the presence of a minimally coupled massless scalarfield. The spacetimes have a $(d-2)$-dimensional base manifold given by anEinstein space and the massless scalar field depends only on the radialcoordinate. The field equations are decoupled in the general case, and can besolved exactly for the cases when either the cosmological constant vanishes orthe base manifold is Ricci flat. We focus on the case of a negativecosmological constant and a Ricci-flat base manifold. The solution has acurvature singularity located at the origin, where also the scalar fielddiverges. Since there is no event horizon surrounding this singularity, thesolution describes a naked singularity dressed with a nontrivial scalar field.This spacetime is an asymptotically locally anti-de Sitter one when theRicci-flat base manifold is locally flat. The asymptotic solution for anarbitrary Einstein base manifold is found and the corresponding mass,calculated through the canonical generator of the time-translation invariance,is shown to be finite. The contribution to the mass from the scalar field atinfinity is also discussed.

Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions